Deriving Measures of Weight and U.S. Coinage From The Geometry of Form

Deriving Measures of Weight and U.S. Coinage From The Geometry of Form

All of what transpired above exposes an outright “lie” perpetrated upon all of humanity regarding the origins of our systems of measures. Some group amongst us by whatever “name””, who remain hidden from view to this day, has been uncloaked by their own works . . . something they never imagined would ever happen.

Deriving Measures of Weight and U.S. Coinage From The Geometry of Form

In The Geometry of Form there is a sequence called “the natural division of unity”. This has its parallel in nature known as “mitosis”, whereby one cell divides equally into two cells which in turn continue dividing. In the diagram above (lower left) we see a cube dividing into 2 cubes, then into 4 cubes, and 8 cubes. At this point the 8 naturally reconstitute into the form of the original (cube).

The circles depicted in the middle on the right hand side are the cross-sections of a sphere as it is shown to divide its volume into 2, 4, and finally into 8 new spheres. This shows a kind of completion in the division process similar to the cube’s divisioning in that the diameters of the 8 new spheres become exactly half the originals allowing any two to fit perfectly within the original one.

Here we’ve seen an original cube divide into 2, 4, and 8 bringing an additional 7 other cubes into existence. Likewise the sphere, after undergoing division into 8 reconfigures with the now 7 “others” as the 8 sphere star-tetrahedron shown in the middle left side of the diagram. When the centers of these spheres are connected what emerges is the form immediately above with its well defined triangular face planes.

To the star tetrahedrons right, at the top, is what I call the “Decahedron”, so named for its 10 triangular face planes. Its 7 vertices model the center points in a system of 7 spheres (shown at its right). At the charts bottom right is the reconfigured star tetrahedron showing just how closely it resembles the Decahedron.

As a consequence of reproducing by the natural division of unity process the Origin-al unit is found to have an inherent potential comprising seven others which can be modeled only in the form of the decahedron. Unitys’ potential is actualized with its division into eight after beginning the whole process by first dividing one into two. The star-tetrahedron models this system of eight. So in a sense, the difference between “unity and its potential”, and “unity and its actualized potential” is really the difference between the Star tetrahedron and the Decahedron. So what does this difference tell us, at least from its geometric point of view?

On first inspection these appear to be two very different forms. And they are, outwardly. The star-tetrahedron is an omni-symmetrical four pointed star in appearance, and for this it was first named by Archimedes. And the asymmetrical decahedron more closely resembles a bi-valve (clam).


Star Tetahedron
Star Tetahedron

But the star-tetrahedron can also be viewed as the equivalent of five tetrahedronal volume domains (a central tetrahedron is encased within the four other tetrahedrons surrounding it). If these same five tetrahedronal sub-system volume domains are arranged differently, as illustrated in the drawing below, then except for the slight gap, the form of the decahedron is found to be very closely embedded in this rearranged star-tetrahedron. Keep in mind that this rearranged star-tetrahedron is still identical to the original in both volume and surface.

Reconfigured Star Tetrahedron
Reconfigured Star Tetrahedron

One of the consequences of the prohibition against “two points occupying the same location” is the establishment of the minimum line. This occurs when two points are in critical proximity to one another and can move no closer. This is the case in both the decahedron and star-tetrahedron. The distance between these sphere center points is the minimum unit of length possible and can be designated as. . . 1.0 lineal-unit.
Now if we look at these two systems as “points” and “lines” rather than spherical domains, and focus on the more distinct picture of these creatures at the heart of each system, what emerges can be seen again in the illustration below.

Star Tetahedron3
Star Tetahedron3

Since each sphere’s diameter is 1.0 lineal unit, each line comprising their internal system counterparts is also 1.0 lineal unit. Knowing this, it is easy to calculate their volumes. The system of seven points as the decahedron is volume 0.6030056…. Written another way this volume is [(𝞍÷2)+1]÷3. The symbol 𝞍 is for “phi”, also known as The Divine Ratio and is found to be governing structures throughout nature. The system of eight points as the star-tetrahedron has a volume equal to 0.5892556…. If these volume quantities are written another way, as they have been below, one can’t help but notice how similar they really are. We can actually see in these volume quantities a reflection of the similarity in their forms:

5+5√1/2/12 = decahedron volume
5×2√1/2/12 = star-tetrahedron volume

The decahedrons’ volume can be read as “five plus the square-root of five together divided by twelve” and the star tetrahedrons’ volume as “five times the square-root of two together divided by twelve”. The difference between them is a volume of:


And Here is the Start of Where This All Gets Really Interesting

Let’s see what happens when we convert these forms of “volume” measures into “weight” measures. We’ll begin by using the Troy ounce, the oldest of our two ounce systems. Thus the .60300566… volume of the decahedron becomes that portion of a 480 “grain” Troy ounce; this is 289.4427191… grains. And the star tetrahedron becomes 282.84271… grains. The difference between them is 6.60000660… grains, a distinct and rather conspicuous quantity.
Here it should be noted for later reference that .013750014… is 1/30,000th of 412.5, and that the star tetrahedrons’ .58925565… is 1/700th. This 412.5 quantity is the gross weight of the U.S. silver dollar.

The equivalent weight of ten decahedra is 6.0300566… troy ounces, which is 2,894.427191… grains. There are 7000 grains in our familiar marketplace (avoirdupois) pound of 16 ounces. Therefore the weight of the ten decahedra is .413489599… of an Av. pound:

2,894.427191… grains / 7000 grains = .413489599…

Let’s now repackage these grains in the form of a regular tetrahedron. Visualize this: the height of this tetrahedron is 1.240693907… and as the comparable diameter of a sphere makes the spheres’ volume .999982893… Moreover, if this tetrahedron is spun on one faceplane into a cone, the cones’ volume becomes .999982893… which is 1.0 unit to a 99.998% approach to perfection.

Earlier we saw a cube divide into 2,4, and then 8 cubes recombining as one cube with eight subunits. The original cubes’ potential of 7 others, like the star-tetrahedron, models as a central cube encased by one other cube on each of its six faces.
If the cube with edge length equal to 1.0, each face plane 1.02, and volume 1.03 divides its volume into two half units then the edge length of each new cube is the cube root of 0.5, which is .793700526… But if the same cube instead divides its 6 unit surface area into two new 3 surface unit cubes then each new cubes edge becomes .707106781… The difference between these two transformations can be modeled by a cube with edge length equal to 1.0, and a cube with edge length equal to .890898718…

.707106781… / .793700526… = .890898718… / 1.0

If the edge-length of the star-tetrahedron is .890898718… then its surface area is 4.124188… and the sum of its edges (or edge-length sum) is 16.03617… Again, these are both “monetary measures” directly from the geometry of form: 412.5 is the gross weight of the U.S. silver dollar; 16.03773… the amount in grams defining the pure gold quantity in the 1792 Coinage Acts’ $10 eagle.
And if.890898718… is a decahedron’s surface area then .4535903… will be its edge measure quantity. This quantity is certainly a power of 453.592370…, or the number of grams in one pound avoirdupois
.4535903… / 453.592370… = .000999996…
This same decahedron will have a volume equal to .05627466… which quantity is also a power of the 270 grain gross weight of the ten dollar eagle coin with respect to the troy ounce:
.05627466… X 480 grains = 27.0118… grains
Multiples of this special .890898718… quantity also show these same “monetary measures” in gram-based units to an accuracy of .9999+:
18X = 16.03617… (pure gold content in eagle)
27X = 24.05426… (pure silver content in dollar)
30X = 26.72696… (gross weight of dollar coin)
Now watch what happens when we model the 412.5 grains of the silver dollar coin using the man-“chosen” quantity literally invented in the 1790s, i.e., the number of grains in a gram (15.432358…) along with the square root of 3. The form that emerges is the cuboid on the left side of illustration below. The 15.432358… edge length is the exact quantity of grains equal to one gram and its volume mirrors the 412.5 grains defining the weight of the U.S. silver dollar. And the 26.729628… square units of area, comprising each one of its four rectangular edges, is that same coin’s weight but this time in grams.

412.5 grains = 26.729628… grams

US Coinage Geometry Image 4
US Coinage Geometry Image 4

The cuboid on the right is proportionally the same as that on the left which shows that if the 31/2 (square root of 3) width measure is replaced by 1.0 unit then the edges of the cuboid’s square face planes become 8.9098672…

By now, what the reader must come to understand is that this is historical “forensic evidence”. It is based upon an irrefutable level of mathematical anomalies which exposes what certainly must be regarded as a magnificent hoax. All of what transpired above exposes an outright “lie” perpetrated upon all of humanity regarding the origins of our systems of measures. Some group amongst us by whatever “name””, who remain hidden from view to this day, has been uncloaked by their own works . . . something they never imagined would ever happen.

~Paul Kasprzycki

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